Finite Group Databasebeta

← C2×#23749949 #34054575

Subgroups — C2×#23749949 #34054575

Order 19072.

468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011885C211yesmaximal, characteristic
2#23749949C218yesmaximal, direct product factor
3C2×#18011844C211yesmaximal, characteristic, complemented
4C2×#18011842C211yesmaximal, characteristic, complemented
5C2×#18011831C211yesmaximal, characteristic, complemented
6C2×#18011831C211yesmaximal, characteristic, complemented
7C2×C22⋊#11924746C211yesmaximal, characteristic, complemented
8C2×#117×C149C211yesmaximal, characteristic, complemented
9C22×D596C2211yescharacteristic
10C22×C22⋊D149—21no—
11C22×#11924746C2211yescharacteristic
12C22×#11924746C2211yescharacteristic
13#18011885—22no—
14#18011885C2214yes—
15C2×C4⋊Dic149C2211yescharacteristic
16C2×#14558713—21no—
17#18011844C2214yescomplemented
18#18011842C2214yescomplemented
19#18011831C2214yescomplemented
20#18011831C2214yescomplemented
21C22⋊#11924746C2214yescomplemented
22C23×C4×C149C2211yescharacteristic
23#117×C149—22no—
24#117×C149C2214yescomplemented
25C2×C4⋊C4×C149C2211yescharacteristic
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C22⋊C4×C149—21no—
28C2×C42×C149—21no—
29C23×D149—21no—
30C2×D596—21no—
31C2×D596—22no—
32C2×D596—22no—
33C2×D596C2312yes—
34C2×C22⋊D149—24no—
35C2×C22⋊D149—44no—
36C22×Dic149—21no—
37C2×#11924746—22no—
38C2×#11924746—22no—
39C2×#11924746C2312yes—
40C2×#11924746C2312yes—
41C4⋊Dic149—21no—
42C4⋊Dic149C2312yes—
43#14558713—24no—
44C24×C149D411yescharacteristic
45C22×C4×C149—22no—
46C22×C4×C149—22no—
47C22×C4×C149—21no—
48C22×C4×C149—21no—
49C22×C4×C149D411yescharacteristic
50C22×C4×C149D412yes—
51C22×C4×C149C2312yes—
52C22×C4×C149C2311yescharacteristic
53C4⋊C4×C149—21no—
54C4⋊C4×C149—21no—
55C4⋊C4×C149C2312yes—
56C4⋊C4×C149C2312yes—
57C22⋊C4×C149—24no—
58C42×C149—24no—
59C22×D149—22no—
60C22×D149—42no—
61C22×D149—42no—
62C22×D149—42no—
63D596—22no—
64D596—22no—
65D596—42no—
66C22⋊D149—48no—
67C2×Dic149—22no—
68C2×Dic149—42no—
69#11924746—22no—
70#11924746—22no—
71C23×C149—22no—
72C23×C149—22no—
73C23×C149—22no—
74C23×C149C2×D412yes—
75C23×C149C2×D411yescharacteristic
76C2×C4×C149—22no—
77C2×C4×C149—24no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—42no—
83C2×C4×C149—42no—
84C2×C4×C149C2×D412yes—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149#4112yes—
87C2×C4×C149#4112yes—
88C2×C4×C149C2411yescharacteristic
89C22×C149—22no—
90C22×C149—22no—
91C22×C149—22no—
92C22×C149—44no—
93C22×C149#12312yes—
94C22×C149#13512yes—
95C22×C149AGL(1,ℤ/8)12yes—
96C22×C149C22×D411yescharacteristic
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—42no—
100C2×D149—84no—
101C4×C149—22no—
102C4×C149—42no—
103C4×C149—42no—
104C4×C149#12312yes—
105C4×C149C2×#4111yescharacteristic
106C4×C149C2×#4111yescharacteristic
107Dic149—42no—
108C2×C149—42no—
109C2×C149#48214yescomplemented
110C2×C149C2×#12311yescharacteristic
111C2×C149C2×#13511yescharacteristic
112C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
113D149—82no—
114C149C2×#48211yescharacteristic, complemented, Sylow
115C2×#482—1491nomaximal, Sylow
116C2×#121—1491no—
117C2×#117D14911yescharacteristic, complemented
118#482—1498no—
119C2×#107—1491no—
120C2×#106—1491no—
121C2×#102—1491no—
122C2×#102—1491no—
123C2×C22⋊C8—1491no—
124C22×D4—2981no—
125C22×D4—1491no—
126C23×C4C2×D14911yescharacteristic
127C22×C8—1491no—
128C22×C8—1491no—
129#121—2982no—
130#121—1494no—
131#117—22no—
132#117C2×D14914yescomplemented
133C2×C4⋊C4—1491no—
134C2×C4⋊C4C2×D14911yescharacteristic
135C2×C4⋊C4C2×D14911yescharacteristic
136C2×C22⋊C4—21no—
137C2×C22⋊C4—2981no—
138C2×C42—21no—
139#107—1494no—
140#106—1494no—
141#102—1494no—
142#102—1494no—
143C22⋊C8—1494no—
144C24—2981no—
145C24C22⋊D14911yescharacteristic
146C2×D4—2984no—
147C2×D4—2981no—
148C2×D4—2982no—
149C2×D4—2982no—
150C2×D4—5964no—
151C2×D4—1492no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—2981no—
157C22×C4C22⋊D14912yes—
158C22×C4C22⋊D14911yescharacteristic
159C22×C4C22×D14912yes—
160C22×C4C22×D14911yescharacteristic
161C2×C8—2982no—
162C2×C8—2982no—
163C2×C8—1492no—
164C2×C8—1492no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—2981no—
168C4⋊C4—1492no—
169C4⋊C4C22×D14912yes—
170C4⋊C4C22×D14912yes—
171C22⋊C4—24no—
172C22⋊C4—2984no—
173C42—24no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—2982no—
178C23—5962no—
179C23—5962no—
180C23—5962no—
181C23C2×C22⋊D14912yes—
182C23C2×C22⋊D14911yescharacteristic
183D4—2982no—
184D4—2982no—
185D4—5968no—
186D4—5962no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—2982no—
196C2×C4—5962no—
197C2×C4C2×C22⋊D14912yes—
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4#1455873612yes—
200C2×C4#1455873612yes—
201C2×C4C23×D14911yescharacteristic
202C8—2982no—
203C8—2982no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—44no—
208C22—5962no—
209C22—5962no—
210C22—5962no—
211C22—11924no—
212C22#1801189412yes—
213C22#1801193112yes—
214C22#1801193612yes—
215C22C22×C22⋊D14911yescharacteristic
216C4—22no—
217C4—42no—
218C4—42no—
219C4—5962no—
220C4#1801189412yes—
221C4C2×#1455873611yescharacteristic
222C4C2×#1455873611yescharacteristic
223C2—42no—
224C2—11922no—
225C2#2374994914yesdirect product factor
226C2C2×#1801189411yescharacteristic
227C2C2×#1801193111yescharacteristic
228C2C2×#1801193611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#117×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011885C2
hypercenterC2×#117D149
hypocenterC149C2×#482
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23749949C2direct (N × H)
3. C2×#18011844C2semidirect
4. C2×#18011842C2semidirect
5. C2×#18011831C2semidirect
6. C2×#18011831C2semidirect
7. C2×C22⋊#11924746C2semidirect
8. C2×#117×C149C2semidirect
17. #18011844C22semidirect
18. #18011842C22semidirect
19. #18011831C22semidirect
20. #18011831C22semidirect
21. C22⋊#11924746C22semidirect
24. #117×C149C22semidirect
109. C2×C149#482semidirect
114. C149C2×#482semidirect
117. C2×#117D149semidirect
132. #117C2×D149semidirect
225. C2#23749949direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180118852
#237499492
C2×#180118442
C2×#180118422
C2×#180118312
C2×C22⋊#119247462
C2×#117×C1492
C2×#482149